{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TGBGFPSPMGITNTCYCUVSAL3YPM","short_pith_number":"pith:TGBGFPSP","canonical_record":{"source":{"id":"1705.07038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-19T15:07:07Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"87c4bdc8df08de76f9e8be6ad5530b5f3253f55e4b7e9f77dcb35c8a54e4c7c6","abstract_canon_sha256":"706ffc541d09cebdd1e74adcb8060ee118001787c516262fd78c7ed4e7a40edb"},"schema_version":"1.0"},"canonical_sha256":"998262be4f619136cc58152b202f787b20c270302ddc762e237e525323b784ff","source":{"kind":"arxiv","id":"1705.07038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07038","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07038v2","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07038","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"TGBGFPSPMGIT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TGBGFPSPMGITNTCY","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TGBGFPSP","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TGBGFPSPMGITNTCYCUVSAL3YPM","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-19T15:07:07Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"87c4bdc8df08de76f9e8be6ad5530b5f3253f55e4b7e9f77dcb35c8a54e4c7c6","abstract_canon_sha256":"706ffc541d09cebdd1e74adcb8060ee118001787c516262fd78c7ed4e7a40edb"},"schema_version":"1.0"},"canonical_sha256":"998262be4f619136cc58152b202f787b20c270302ddc762e237e525323b784ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:35.625734Z","signature_b64":"uAo2NrzMKoAVSJeNpJ7QgvqWAB42RvgqjLgFUXaPQGwtNKGjpgAbOEKgHjJ+0+tbAgM8z06lfImDXz7TIP7GDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"998262be4f619136cc58152b202f787b20c270302ddc762e237e525323b784ff","last_reissued_at":"2026-05-18T00:38:35.625341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:35.625341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07038","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aaOCiI0k3fIPPCTge9ugNxCtSgpgIqrwZCQPdghPrjcXP8KDVQJ6y62GCJ9GjxvpJ3OxHiwDljel5p6s6M6HDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:29:50.009709Z"},"content_sha256":"f02b02c70dffb689254d3815b23ab19f0def04bb1309f31218ae470b11f72602","schema_version":"1.0","event_id":"sha256:f02b02c70dffb689254d3815b23ab19f0def04bb1309f31218ae470b11f72602"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TGBGFPSPMGITNTCYCUVSAL3YPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Landscape of Deep Learning Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Jiashi Feng, Pan Zhou","submitted_at":"2017-05-19T15:07:07Z","abstract_excerpt":"This paper studies the landscape of empirical risk of deep neural networks by theoretically analyzing its convergence behavior to the population risk as well as its stationary points and properties. For an $l$-layer linear neural network, we prove its empirical risk uniformly converges to its population risk at the rate of $\\mathcal{O}(r^{2l}\\sqrt{d\\log(l)}/\\sqrt{n})$ with training sample size of $n$, the total weight dimension of $d$ and the magnitude bound $r$ of weight of each layer. We then derive the stability and generalization bounds for the empirical risk based on this result. Besides,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07038","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"95IaUvIi95vWPd0E7BXimkV/XoEHg8efQ87p4gV6nWNG1MSNlRlzCPUlfP1nAh7P4UXg3UNDPXJsQbkN4SVMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:29:50.010060Z"},"content_sha256":"0049cfca636d721a718cdc2ac2fa08c5823c704c2b0f7da66a0cf7e12c0e2f04","schema_version":"1.0","event_id":"sha256:0049cfca636d721a718cdc2ac2fa08c5823c704c2b0f7da66a0cf7e12c0e2f04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGBGFPSPMGITNTCYCUVSAL3YPM/bundle.json","state_url":"https://pith.science/pith/TGBGFPSPMGITNTCYCUVSAL3YPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGBGFPSPMGITNTCYCUVSAL3YPM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T16:29:50Z","links":{"resolver":"https://pith.science/pith/TGBGFPSPMGITNTCYCUVSAL3YPM","bundle":"https://pith.science/pith/TGBGFPSPMGITNTCYCUVSAL3YPM/bundle.json","state":"https://pith.science/pith/TGBGFPSPMGITNTCYCUVSAL3YPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGBGFPSPMGITNTCYCUVSAL3YPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TGBGFPSPMGITNTCYCUVSAL3YPM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"706ffc541d09cebdd1e74adcb8060ee118001787c516262fd78c7ed4e7a40edb","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-19T15:07:07Z","title_canon_sha256":"87c4bdc8df08de76f9e8be6ad5530b5f3253f55e4b7e9f77dcb35c8a54e4c7c6"},"schema_version":"1.0","source":{"id":"1705.07038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07038","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07038v2","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07038","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"TGBGFPSPMGIT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TGBGFPSPMGITNTCY","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TGBGFPSP","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:0049cfca636d721a718cdc2ac2fa08c5823c704c2b0f7da66a0cf7e12c0e2f04","target":"graph","created_at":"2026-05-18T00:38:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper studies the landscape of empirical risk of deep neural networks by theoretically analyzing its convergence behavior to the population risk as well as its stationary points and properties. For an $l$-layer linear neural network, we prove its empirical risk uniformly converges to its population risk at the rate of $\\mathcal{O}(r^{2l}\\sqrt{d\\log(l)}/\\sqrt{n})$ with training sample size of $n$, the total weight dimension of $d$ and the magnitude bound $r$ of weight of each layer. We then derive the stability and generalization bounds for the empirical risk based on this result. Besides,","authors_text":"Jiashi Feng, Pan Zhou","cross_cats":["cs.LG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-19T15:07:07Z","title":"The Landscape of Deep Learning Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07038","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f02b02c70dffb689254d3815b23ab19f0def04bb1309f31218ae470b11f72602","target":"record","created_at":"2026-05-18T00:38:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"706ffc541d09cebdd1e74adcb8060ee118001787c516262fd78c7ed4e7a40edb","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-19T15:07:07Z","title_canon_sha256":"87c4bdc8df08de76f9e8be6ad5530b5f3253f55e4b7e9f77dcb35c8a54e4c7c6"},"schema_version":"1.0","source":{"id":"1705.07038","kind":"arxiv","version":2}},"canonical_sha256":"998262be4f619136cc58152b202f787b20c270302ddc762e237e525323b784ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"998262be4f619136cc58152b202f787b20c270302ddc762e237e525323b784ff","first_computed_at":"2026-05-18T00:38:35.625341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:35.625341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uAo2NrzMKoAVSJeNpJ7QgvqWAB42RvgqjLgFUXaPQGwtNKGjpgAbOEKgHjJ+0+tbAgM8z06lfImDXz7TIP7GDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:35.625734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f02b02c70dffb689254d3815b23ab19f0def04bb1309f31218ae470b11f72602","sha256:0049cfca636d721a718cdc2ac2fa08c5823c704c2b0f7da66a0cf7e12c0e2f04"],"state_sha256":"c9374eeb1e3c38997073f1fb7a58500d27fd270360b90abf8f20f70cd7c5c037"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCY23ZpiTXB4+GPUqsoVq3hXOrHMrVtHhiQfivD2Zkkm2zw60n8NmIOOjEezqHGAkI/dy8j81Un7d6BtLj8SDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:29:50.012057Z","bundle_sha256":"659150c82c08c0e79f0484d791e9a360e5dce03a74e4049ecc946f0aae8376db"}}